The nation's largest mobile carrier announced earlier this week that beginning in October, that the 5% of 4G LTE device users with unlimited data plans may see some slower connectivity to help Verizon better optimize its network.

"They may experience slower data speeds when using certain high bandwidth applications, such as streaming high-definition video or during real-time, online gaming, and only when connecting to a cell site when it is experiencing heavy demand," the notice reads on the company website.

In a letter today, Wheeler questioned whether such a practice would stand the agency's rules on allowable speed reductions. "I know of no past Commission statement that would treat as 'reasonable network management' a decision to slow traffic to a user who has paid, after all, for 'unlimited' service," Wheeler wrote in the letter.

The chairman asked Verizon president and CEO Daniel Mead for the company's rationale and how it justifies the planned action under rules the company agreed to in bidding for the spectrum its wireless service uses.

It's the first time the chairman has asked a carrier about this particular form of "network management," which falls under part of the FCC's Open Internet rules that remain in effect. A federal appeals court in January struck down much of the agency's rules regarding Internet traffic being treated equally.

In its online note, Verizon said that most data customers would not see any impact from the new policy.

"We understand that our customers rely on their smartphones and tablets every day. Our network optimization policy provides the best path to ensure a continued great wireless experience for all of our customers on the best and largest wireless network in the U.S.," the company's vice president for technology, Mike Haberman, said in the notice.

Verizon Wireless has attempted to lure subscribers from unlimited data plans with plans that make it cheaper to get new smartphones and have data allowances.